Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101380
Title: On representation formulas for solutions of linear differential equations with Caputo fractional derivatives
Authors: Gomoyunov, M. I.
Issue Date: 2020
Publisher: De Gruyter Open Ltd
Citation: Gomoyunov M. I. On representation formulas for solutions of linear differential equations with Caputo fractional derivatives / M. I. Gomoyunov. — DOI 10.1515/fca-2020-0058 // Fractional Calculus and Applied Analysis. — 2020. — Vol. 23. — Iss. 4. — P. 1141-1160.
Abstract: In the paper, a linear differential equation with variable coefficients and a Caputo fractional derivative is considered. For this equation, a Cauchy problem is studied, when an initial condition is given at an intermediate point that does not necessarily coincide with the initial point of the fractional differential operator. A detailed analysis of basic properties of the fundamental solution matrix is carried out. In particular, the Hölder continuity of this matrix with respect to both variables is proved, and its dual definition is given. Based on this, two representation formulas for the solution of the Cauchy problem are proposed and justified. © 2020 Diogenes Co., Sofia.
Keywords: AND PHRASES: LINEAR FRACTIONAL DIFFERENTIAL EQUATION
FUNDAMENTAL SOLUTION MATRIX
REPRESENTATION FORMULA
URI: http://hdl.handle.net/10995/101380
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85092916604
PURE ID: 14148798
11461f08-081e-48d6-b1b0-cbb087b45a34
ISSN: 13110454
DOI: 10.1515/fca-2020-0058
metadata.dc.description.sponsorship: This work was supported by RSF, Project No 19-11-00105.
RSCF project card: 19-11-00105
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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